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Geometric measure of entanglement and applications to bipartite and multipartite quantum states
Open accessAbstract
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, 675 (1995); H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, 6787 (2001)], is explored for bipartite and multipartite pure and mixed states. The measure is determined analytically for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states. In particular, a detailed analysis is given for arbitrary mixtures of three-qubit Greenberger-Horne-Zeilinger, W, and inverted-$W$ states. Along the way, we point out connections of the geometric measure of entanglement with entanglement witnesses and with the Hartree approximation method.
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Metadata
- Authors
- Wei, T.-C., & Goldbart, P. M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-10-09
- Volume
- 68
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1973912509
- Cited by
- 742
- References
- 31
- FWCI
- 15.19
- Type
- journal article
- Language
- en
- Open access
- green
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